The sobol sensitivity analysis of the pressure, stresses, and displacement arising from poroelastic modelling of hard mechanical systems

We perform a sensitivity analysis to investigate the influence of material input parameters on the pressure, stresses, and displacement of an isotropic porous solid cylinder representing hard mechanical systems such as the bone. We model the system using the governing equations of Biot’s poroelasticity in cylindrical polar coordinates, where the solutions are found by enforcing radial boundary conditions. The sensitivity analysis is carried out on the solutions for the pressure, stress components and displacement using ranges of the investigated parameters representative of the bone. Our study finds that the time t * has the highest influence on the pressure, the stress components and displacements. We find that the Poisson ratio ν plays a greater role than shear µ in the pressure response, and the shear µ counts more than the other parameters in the radial and circumferential stresses. There are key joint interactions between the Biot’s coefficient α and the Poisson ratio ν, the non-dimensionalised radius R * of the bone, and the Biot’s modulus M when investigating interstitial pressure, which is a key value in bone remodelling and fracture healing. This study paves the way to a deeper understanding of the interplay of all the parameters that are necessary to capture the true behaviour of hard mechanical systems such as the bone and its potential remodelling.